Watch the Blues: Technique 9 online guitar lesson by Robbie Calvo from RhythmCraft
Walking basslines are more often than not derived from chord arpeggios. So, when you or your bass player want to create walking lines that's the best place to start. What you are doing is defining the harmony with the notes found in the chords only this time it's below the chords in pitch rather than above them in pitch, as in lead guitar improvisation. Of course you can add in other tones for flavor. My advice here would be sing a part and when you come up with something you like transpose that onto your guitar or bass.
For this example I am copying the notes I actually played for the walking bass part you've been playing over up to this point. Why should we be able to play this as guitarists? Well, if you've been learning your arpeggios it will be no big deal for starters! If you ever want to pick up the bass at a jam session or studio you'll know what to do. Lastly, doubling parts sounds cool especially an octave apart. Also, if there's a keyboard player and another guitarist in the band or recording, you may want to simplify your part to let everything work together as an ensemble and using single note lines can help with this.
Have fun playing this on the guitar and if you have access to a bass, give it a try using your fingers instead of a pick.